New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance

Details New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance

2002-01-13

arxiv.org/abs/hep-th/0201080v1

J.Phys.A35:1389-1404,2002

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, Latex, Journal of Physics A, to be published

Scientific paper

10.1088/0305-4470/35/6/305

Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations of Higher order SUSY Quantum Mechanics (HSUSY QM) with supercharges allowing for separation of variables. 2)The second one is a generalization of shape invariance. While in one dimension shape invariance allows to solve algebraically a class of (exactly solvable) quantum problems, its generalization to higher dimensions has not been yet explored. Here we provide a formal framework in HSUSY QM for two-dimensional quantum mechanical systems for which shape invariance holds. Given the knowledge of one eigenvalue and eigenfunction, shape invariance allows to construct a chain of new eigenfunctions and eigenvalues. These methods are applied to a two-dimensional quantum system, and partial explicit solvability is achieved in the sense that only part of the spectrum is found analytically and a limited set of eigenfunctions is constructed explicitly.

Affiliated with

Also associated with

No associations

Rating

New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-656722